(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 =...
(a) Find and identify the traces of the quadric surface
x2 + y2 ? z2 = 25
given the plane.
x = k
Find the trace.
Identify the trace.
y=k
Find the trace.
Identify the trace.
z=k
Find the trace
Identify the trace.
(b) If we change the equation in part (a) to
x2 ? y2 + z2 = 25,
how is the graph affected?
(c) What if we change the equation in part (a) to
x2 + y2 + 2y ? z2 = 24?
Homework Answers
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(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 =...
(a) Find and identify the traces of the quadric surface x2 + y2 − z2 =...
(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 16 given the plane. x = k Find the trace. Identify the trace. circleellipse hyperbolaparabola y = k Find the trace. Identify the trace. circleellipse hyperbolaparabola z = k Find the trace. Identify the trace. circleellipse hyperbolaparabola Describe the surface from one of the graphs in the table. ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets (b) If we change the equation in part (a) to...
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(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 =...
(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 = 16 given the plane. x = k Find the trace. y = k Find the trace. z = k Find the trace. Describe the surface from one of the graphs in the table. ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets
Exercise 3. Find and identify the trace of the given quadric surface in the specified plane...
Exercise 3. Find and identify the trace of the given quadric surface in the specified plane of coordinates. f) x2 + 2y – 2z2 – 2 = 0, xz-plane. g) x = y2 + 4, xy-plane. a) A + B + * = 1, xy-plane. b) x2 + 4y2 – 4z2 – 16 = 0, xz-plane. c) -4x2 - y2 + z2 = 1, yz-plane. d) x2 + – z2 = 0, yz-plane. e) x2 + x2 – 4y+4= 0,...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch th...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard...
16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard form: SOLUTION z2 16 4 Comparing this equation with equations of quadratic surfaces, we see that it represents a hyperboloid of two sheets the only difference being that in this case the axis of the hyperboloid is the y-axis The traces in the xy and yz-planes are the hyperbolas 16 and z2 =1 4 x=0. 16 The surface has...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone ...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
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7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of...
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 +...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the pa...
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
Exercise 3. Find and identify the trace of the given quadric surface in the specified plane of coordinates. f) x2 + 2y – 2z2 – 2 = 0, xz-plane. g) x = y2 + 4, xy-plane. a) A + B + * = 1, xy-plane. b) x2 + 4y2 – 4z2 – 16 = 0, xz-plane. c) -4x2 - y2 + z2 = 1, yz-plane. d) x2 + – z2 = 0, yz-plane. e) x2 + x2 – 4y+4= 0,...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard form: SOLUTION z2 16 4 Comparing this equation with equations of quadratic surfaces, we see that it represents a hyperboloid of two sheets the only difference being that in this case the axis of the hyperboloid is the y-axis The traces in the xy and yz-planes are the hyperbolas 16 and z2 =1 4 x=0. 16 The surface has...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
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